Thermal barrier coating (TBC) systems have come to be widely used, particularly with respect to aircraft engines and industrial gas turbines. TBC systems typically include a coating of non-conductive material, such as ceramic, secured to a metal part, such as a turbine blade or a turbine vane, by a bonding coat. The ceramic coating insulates the metal part from hot combustion gases. Further insulation is typically provided by cooling holes, which are drilled through the part to provide a film of air on surfaces exposed to hot combustion gases. Known methods of manufacturing the cooling holes (e.g., laser drilling, abrasive water jets) can be very expensive or difficult to perform with requisite accuracy. Moreover, these methods may damage the ceramic coating. Accordingly, a cost effective and accurate method of machining cooling holes through thermal barrier coated parts is desired.